Triangle QRS has 3 congruent sides, so it is equilateral and equiangular.
The sum of the measures of the angles of a triangle is 180 deg, so each angle of triangle QRS is 60 deg.
Angle RQS measures 60 degrees and forms a linear pair with angle PQS. Angles in a linear pair a supplementary. That makes the measure of angle PQS 120 deg. leaving only 60 degrees as the sum of the measures of angles PSQ and SPQ. Triangle PQS is isosceles since sides PQ and QS are congruent. The angles opposite congruent sides of a triangle are congruent, so angle PSQ is congruent to angle SPQ. That means angles PSQ and SPQ measure 30 deg each.
m<PSR = m<PSQ + m<QSR = 30 + 60 = 90
m<PQS = 120
m<PSR : m<PQS = 90 : 120 = 3 : 4
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